Q5.13 new system will require much less labor. What would be the impact of this system on the ordering pattern? [5.6] (Powered by Koffee) Powered by Koffee (PBK) is a new campus coffee store. PBK uses 50 bags of whole bean coffee every month, and you may assume that demand is perfectly steady throughout the year. PBK has signed a year-long contract to purchase its coffee from a local supplier, Phish Roasters, for a price of $25 per bag and an $85 fixed cost for every delivery independent of the order size. The holding cost due to storage is $1 per bag per month. PBK managers figure their cost of capital is approximately 2 percent per month. a. What is the optimal order size, in bags? [5.6] b. Given your answer in (a), how many times a year does PBK place orders? [5.6] c. Given your answer in (a), how many months of supply of coffee does PBK have on average? [5.6] d. On average, how many dollars per month does PBK spend to hold coffee (including cost of capital)? [5.6] Suppose that a South American import/export company has offered PBK a deal for the next year. PBK can buy a year's worth of coffee directly from South America for $20 per bag and a fixed cost for delivery of $500. Assume the estimated cost for inspection and storage is $1 per bag per month and the cost of capital is approximately 2 percent per month. e. Should PBK order from Phish Roasters or the South American import/export com- pany? Quantitatively justify your answer. [5.6] Q5.5 Processing Time: 0.25 Minute/Part Setup Time: 30 Minutes Processing Time: 0.20 Minute/Part Setup Time: 20 Minutes Processing Time: 0.15 Minute/Part Setup Time: 45 Minutes Work is processed in batches at each step. Before a batch is processed at a step, the machine at that step must be set up. (During a setup, the machine is unable to process any product.) Assume that there is a dedicated setup operator for each machine (i.e., there is always someone available to perform a setup at each machine.) a. What is the capacity of step 1 if the batch size is 35 parts? [5.6] b. For what batch sizes is step 1 (2, 3) the bottleneck? [5.6] (JCL Inc.) JCL Inc. is a major chip manufacturing firm that sells its products to com- puter manufacturers like Dell, HP, and others. In simplified terms, chip making at JCL Inc. involves three basic operations: depositing, patterning, and etching. . Depositing: Using chemical vapor deposition (CVD) technology, an insulating mate- rial is deposited on the wafer surface, forming a thin layer of solid material on the chip. . Patterning: Photolithography projects a microscopic circuit pattern on the wafer sur- face, which has a light-sensitive chemical like the emulsion on photographic film. It is repeated many times as each layer of the chip is built. . Etching: Etching removes selected material from the chip surface to create the device structures. The following table lists the required processing times and setup times at each of the steps. Assume that the unit of production is a wafer, from which individual chips are cut at a later stage. Note: A setup can only begin once the batch has arrived at the machine. Process Step 20 min. 1 Depositing 45 min. 2 Patterning 3 Etching Processing time 0.15 min./unit 30 min. 0.25 min./unit 0.20 min./unit Setup time Q5.6 a. What is the process capacity in units per hour with a batch size of 100 wafers? [5.1] b. For what batch size is step 3 (etching) the bottleneck? [5.6] c. Suppose JCL Inc. came up with a new technology that eliminated the setup time for step 1 (deposition), but increased the processing time to 0.45 minute/unit. What would be the batch size you would choose so as to maximize the overall capacity of the pro- cess? [5.6] (Kinga Doll Company) Kinga Doll Company manufactures eight versions of its popular girl doll, Shari. The company operates on a 40-hour workweek. The eight versions differ in doll skin, hair, and eye color, enabling most children to have a doll with a similar appear- ance to them. It currently sells an average of 4,000 dolls (spread equally among its eight versions) per week to boutique toy retailers. In simplified terms, doll making at Kinga involves three basic operations: molding the body and hair, painting the face, and dressing the doll. Changing over between versions requires setup time at the molding and painting stations due to the different colors of plastic pellets, hair, and eye color paint required. Q9.5 Q9.6 Assume that there are no limits on the number of customers that can be on hold and that customers do not hang up even if forced to wait a long time. a. For one of his courses, Tom has to read a book (The Pole, by E. Silvermouse). He can read 1 page per minute. Tom's boss has agreed that Tom could use his idle time for studying, as long as he drops the book as soon as a call comes in. How many pages can Tom read during an 8-hour shift? [9.5] b. How long does a customer have to wait, on average, before talking to Tom? [9.5] c. What is the average total cost of telephone lines over an 8-hour shift? Note that the department store is billed whenever a line is in use, including when a line is used to put customers on hold. [9.5] (Atlantic Video) Atlantic Video, a small video rental store in Philadelphia, is open 24 hours a day, and-due to its proximity to a major business school-experiences cus- tomers arriving around the clock. A recent analysis done by the store manager indicates that there are 30 customers arriving every hour, with a standard deviation of interarrival times of 2 minutes. This arrival pattern is consistent and is independent of the time of day. The checkout is currently operated by one employee, who needs on average 1.7 minutes to check out a customer. The standard deviation of this checkout time is 3 minutes, primarily as a result of customers taking home different numbers of videos. a. If you assume that every customer rents at least one video (i.e., has to go to the check- out), what is the average time a customer has to wait in line before getting served by the checkout employee, not including the actual checkout time (within 1 minute)? [9.5] b. If there are no customers requiring checkout, the employee is sorting returned vid- cos, of which there are always plenty waiting to be sorted. How many videos can the employee sort over an 8-hour shift (assume no breaks) if it takes exactly 1.5 minutes to sort a single video? [9.5] c. What is the average number of customers who are at the checkout desk, either waiting or currently being served (within I customer)? [9.5] d. Now assume for this question only that 10 percent of the customers do not rent a video at all and therefore do not have to go through checkout. What is the average time a cus- tomer has to wait in line before getting served by the checkout employee, not including the actual checkout time (within 1 minute)? Assume that the coefficient of variation for the arrival process remains the same as before. [9.5] e. As a special service, the store offers free popcorn and sodas for customers waiting in line at the checkout desk. (Note: The person who is currently being served is too busy with paying to eat or drink.) The store owner estimates that every minute of customer waiting time costs the store 75 cents because of the consumed food. What is the optimal number of employees at checkout? Assume an hourly wage rate of $10 per hour. [9.8] (RentA Phone) RentAPhone is a new service company that provides European mobile phones to American visitors to Europe. The company currently has 80 phones available at Charles de Gaulle Airport in Paris. There are, on average, 25 customers per day requesting a phone. These requests arrive uniformly throughout the 24 hours the store is open. (Note: This means customers arrive at a faster rate than 1 customer per hour.) The corresponding coefficient of variation is 1. Customers keep their phones on average 72 hours. The standard deviation of this time is 100 hours. Given that RentAPhone currently does not have a competitor in France providing equally good service, customers are willing to wait for the telephones. Yet, during the waiting period, customers are provided a free calling card. Based on prior experience, RentAPhone found that the company incurred a cost of $1 per hour per waiting customer. night